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How random numbers improve weather and climate predictions Expected and unexpected effects of stochastic parameterizations NCAR day of networking and.

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Presentation on theme: "How random numbers improve weather and climate predictions Expected and unexpected effects of stochastic parameterizations NCAR day of networking and."— Presentation transcript:

1 How random numbers improve weather and climate predictions Expected and unexpected effects of stochastic parameterizations NCAR day of networking and discovery, April, 17, 2015 Judith Berner

2 With contributions from: Dani Coleman, Hannah Christensen, Kate Fossell, Soyoung Ha, Josh Hacker, Glen Romine, Craig Schwartz, Chris Snyder Felipe Tagle

3 Mean systematic error of 500 hPa geopotential height fields
LOWRES HIGHRES

4 Mean systematic error of 500 hPa geopotential height fields
LOWRES HIGHRES SKEBS Reduction of z500 bias in all simulations with model-refinement Berner et al., 2012

5 Potential of stochastic parameterizations to reduce model error
Weak noise Multi-modal Unimodal Ball in double-potential well PDF Strong noise

6 Potential of stochastic parameterizations to reduce model error
Weak noise Multi-modal Unimodal Potential PDF Strong noise

7 Potential of stochastic parameterizations to reduce model error
Weak noise Multi-modal Unimodal Potential PDF Stochastic parameterizations can change the mean and variance of a PDF Impacts variability Impacts mean bias Strong noise

8 Key message Random numbers can improve weather and climate predictions

9 Outline The stochastic parameterization schemes
Climate application: Impact in coupled and uncoupled simulations with the Earth System Model CESM Weather application: Improving reliability and reducing analysis error in cycled and uncycled forecasts with the weather model WRF

10 Stochastically perturbed tendency scheme (SPPT)
Rationale: Especially as resolution increases, the equilibrium assumption is no longer valid and fluctuations of the subgrid-scale state should be sampled (Buizza et al. 1999, Palmer et al. 2009, Berner et al. 2014) Local tendency for variable X Dynamical tendencies => Resolved scales Physical tendencies => Unresolved scales Perturbs accumulated U,V,T,Q tendencies from physical parameterizations packages Same pattern for all tendencies to minimize introduction of imbalances

11 Stochastic-kinetic energy backscatter scheme (SKEBS)
Rationale: A fraction of the subgrid-scale energy is scattered upscale and acts as random streamfunction and temperature forcing for the resolved-scale flow (Shutts 2005, Berner et. al 08,09). Here simplified version with constant dissipation rate: can be considered as additive noise with spatial and temporal correlations. Stochastic Forcing Pattern Local tendency for variable X =U,V,T Dynamical tendencies => Resolved scales Physical tendencies => Unresolved scales Additive stochastic perturbation tendencies => Unresolved scales

12 Outline The stochastic parameterization schemes
Climate application: Impact in coupled and uncoupled simulations with the Earth System Model CESM Weather application: Improving reliability and reducing analysis error in cycled and uncycled forecasts with the weather model WRF

13 Northern Annular Mode (MAM) 1st EOF of sea level pressure over Northern Hemispheric Extratropics
NCEP SKEBS CNTL SPPT 21% 50% 35% 37% CAM4 AMIP simulations (prescribed SSTs), Stochastic parameterization improves pattern and reduces explained variance Degenerate response: SKEBS and SPPT have same effect

14 Northern Annular Mode (MAM) 1st EOF of sea level pressure over Northern Hemispheric Extratropics
NCEP SKEBS CNTL SPPT 21% 50% 35% 37% CAM4 AMIP simulations (prescribed SSTs), Stochastic parameterization improves pattern and reduces explained variance Degenerate response: SKEBS and SPPT have same effect

15 Sketch: CAM4 behavior Including a stochastic parameterization does not lead to large changes in the pattern of modes of variability, but to decreased explained variances This is consistent with a flattening of a potential well Stochastic parameterizations can also lead to a depending of a potential well. Potential without stochastic perturbations Potential with stochastic perturbations

16 Sketch: CAM4 behavior Including a stochastic parameterization does not lead to large changes in the pattern of modes of variability, but to decreased explained variances This is consistent with a shallowing of a potential well Stochastic parameterizations can also lead to a depending of a potential well. Potential without stochastic perturbations Potential with stochastic perturbations

17 First EOF of 500hPa-field over Atlantic sector
NCEP 49% 44% CNTL SKEBS 46% SPPT 53%

18 First EOF of 500hPa-field over Atlantic sector
NCEP 49% 44% CNTL SKEBS 46% SPPT 53%

19 Impact of SPPT on sea surface temperature (SST) variability
Coupled simulations with CAM4, Too much variability in SSTs in Tropical Pacific SPPT reduces bias in SST variability in Tropical Pacific How can a stochastic parameterization reduce variability?

20 Impact of SPPT on sea surface temperature (SST) variability
How can perturbations to the atmosphere improve the ocean? SPPT reduces variability in u850 variability over the Western Pacific

21 Impact of SPPT on El Niño Southern Oscillation

22 Probability density function of daily temperatures over North America (JJA)
AMIP simulations with CAM4 Too much variability in daily temperatures in summer compared to reanalysis

23 General extreme value distributions fitted to annual monthly temperature maxima and minima
Tagle et al. 2015 CAM4 has to high return values for both, TMAX and TMIN Overestimation of extreme temperatures SKEBS and deteriorates 20yr return values for TMAX, but slightly improves values for TMIN

24 Impact of SKEBS on precipitation bias
Coupled control run shows significant bias due to split inter-tropical convergence zone SKEBS reduced bias in precipitation

25 Outline The stochastic parameterization schemes
Climate application: Impact in coupled and uncoupled simulations with the Earth System Model CESM Weather application: Improving reliability and reducing analysis error in cycled and uncycled forecasts with the weather model WRF

26 Representing initial uncertainty by an ensemble of states
Forecast uncertainty in weather models: Initial condition uncertainty Model uncertainty Boundary condition uncertainty Represent initial forecast uncertainty by ensemble of states Reliable forecast system: Spread should grow like ensemble mean error Predictable states with small error should have small spread Unpredictable states with large error should have large spread \ RMS error spread ensemble mean analysis

27 Spread and error near the surface
Solid lines: rms error of ensemble mean Dashed: spread Ensemble is underdispersive (= not enough spread) Unreliable and over-confident Depending on cost-loss ratio potentially large socio-economic impact (e.g. should roads be salted)

28 Brier skill score near the surface
Brier skill measures probabilistic skill in regard to a reference (here CNTL). Verified event: μ<x<μ+σ Berner et al., et al 2015

29 Reliability diagram for rain-thresholds, averaged over forecast hours 18–36 using a 50-km neighborhood Romine et al., 2014

30 WRF-DART: Verification of surface analysis against independent observations
V-10m T-2m Analysis rms errors in D2: SP < MP < CP in surface winds while MP is better than SP in T2. Including a model-error representation reduces the RMS error of the surface analysis (also prior) in 10m wind and Temperature at 2m CNTL SKEBS PHYS Ha et al. 2015

31 Sketch: WRF behavior Verifying observation Including a stochastic parameterization increased ensemble spread In cycled forecasts is reduces the mean analysis error Potential without stochastic perturbations Potential with stochastic perturbations

32 Debate in the field: A priori vs a posteriori
Model uncertainty added a posteriori: Model Forecast uncertainty Process uncertainty added a priori during model development: Stochasticity

33 Conclusions Random numbers can improve weather and climate predictions
by impacting variability and mean in expected (increase variability) and unexpected (decrease variability) ways

34 Thank you! Berner, J, K. Fossell, S.-Y. Ha, J. P. Hacker, C. Snyder 2015: “Increasing the skill of probabilistic forecasts: Understanding performance improvements from model-error representations, Mon. Wea. Rev., 143, Berner, J., S.-Y. Ha, J. P. Hacker, A. Fournier, C. Snyder, 2011: “Model uncertainty in a mesoscale ensemble prediction system: Stochastic versus multi-physics representations” , Mon. Wea. Rev, 139, Romine, G. S., C. S. Schwartz, J. Berner, K. R. Smith, C. Snyder, J. L. Anderson, and M. L. Weisman, 2014: “Representing forecast error in a convection-permitting ensemble system”, Mon. Wea. Rev, 142, 12, 4519–4541 Ha, S.-Y., J. Berner, C. Snyder, 2015: “Model-error representation in mesoscale WRF-DART cycling”, under review at Mon. Wea. Rev.

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